Bayesian Model Selection
Three sided coin
Model 1: Surface Area
\[p(h, R) = \frac{2\pi R h}{2\pi R^2 + 2\pi Rh}\]
\[p(\eta) = \frac{\eta}{1 + \eta}\]
Model 2: Cross-sectional Length
\[ p(h, R) = \frac{h}{2(2R) + h}\] \[ p(\eta) = \frac{\eta}{4 + \eta} \]
Model 3: Cross-sectional angle
Model 3: Cross-sectional angle
Model 3: Cross-sectional angle
\[ p(\eta) = \frac{\arctan (\eta/2)}{\arctan(\eta/2) + \arctan(2/\eta)} \]
Model 4: Spherical Surface Area
\[ p(\eta) = \,? \]
MCMC: Gibbs Sampling
Changepoint problem
